Nonlinear Structural Response Research Articles

Detection of Nonlinearity in Photonic Lattices

AbstractAlthough periodic photonic structures, especially associated with nonlinearity, play a prominent role in optics nowadays, effective detection of their nonlinearity still remains a critical challenge. Here, an approach is proposed to detect the nonlinearity of photonic lattices in a direct way. By properly launching structured beams, namely Airy beams, into the lattices, the nonlinear response function of the discrete system can be directly obtained in the nonlinearly‐shaped beam profiles. To be specific, a single Airy beam is utilized to map self‐defocusing nonlinearity, while self‐focusing nonlinearity, which is hard to visualize in the bulk case, is readily discerned by employing double Airy beams in photonic structures. The proposed method is validated numerically and experimentally by detecting different types of nonlinearities of photonic lattices fabricated in a nonlinear crystal. These findings introduce a promising route for characterizing the nonlinear response of optical structures, thereby broadening the scope of nonlinear measurement and is expected to be extended into other periodic photonic structures.

Nonlinear structural responses of the buried oval steel pipelines crossing strike-slip faults

The permanent ground deformation may lead to bending failure or fractures of the buried steel pipelines. In practical applications, the buried pipelines may also exhibit ovality defects due to soil pressure, gravity of the pipeline, and misalignment of joints, which have the potential to diminish the load-bearing capacity of the buried pipelines. This paper introduces a comprehensive analytical methodology to examine the dynamic behavior of pipelines with different initial ovality defects subjected to strike-slip faults. A modified permissible lateral displacement function is introduced to determine the strain distribution of the deformed pipelines. One may predict the yield displacement of the oval pipelines accurately based on the yield theory of classical beams and the static equilibrium method. Then, the accuracy of the proposed method was validated by developing a finite element model and other results. Good agreement was reached characterized by the yield displacement and the yield strain, respectively. Finally, a parametric analysis was conducted on the effects of different ovality, steel grades, diameter-to-thickness ratios, fault inclination angles, and soil properties on the displacement and strain distributions of the deformed pipeline.

Open-loop swept frequency response of nonlinear structures subjected to weak coupling

AbstractThe present study demonstrates a common behaviour of a forced nonlinear structure with smooth nonlinearity, while coupled dynamics are apparent, originating from the attached electrodynamic shaker. This appears as a variation in the transmitted forcing amplitude and is often subjected to a hysteretic (multi-state) behaviour for up and down open-loop sweeping. This situation differs from the ideal constant amplitude harmonic excitation, on which parameter extraction and engineering comprehension are based on. Untreated or ignored, this can lead to the misinterpretation of the underlying dynamics through the measured nonlinear frequency response curves and their force-normalised version, often called quasi-frequency response function. In this paper, a post-processing solution is introduced for the correct interpretation of frequency response curves at constant forcing amplitudes through the open-loop construction and resectioning of the so-called frequency response surface. The phenomenon and the proposed methodology are demonstrated using a two-degrees-of-freedom model on a shaker-nonlinear beam structure. First, open-loop frequency sweeps are executed on the mechanical system to create the nonlinear frequency response surface, where their actual amplitudes and hysteresis widths are significantly different from the ideal constant forcing amplitude case. The response surface is then sectioned at the assumed constant forcing values by using an appropriate interpolation law. These resectioned curves represent the forced nonlinear standalone structure under ideal constant harmonic excitation. The frequency response surfaces are characterised and resectioned on a nonlinear structure with stiffening and softening cases. Furthermore, an improvement in the operational resonance decay (ORD) method in its filtering and automation is shown to extract the backbone curves (BBCs). The BBC and the resectioned surface provide a complete picture and cross-validation of the underlying dynamics. Finally, the BBC and its distortion are also shown in the response surfaces in relation with the excitation normalization.

An adaptive physics-informed deep learning approach for structural nonlinear response prediction

An adaptive physics-informed deep learning approach for structural nonlinear response prediction

Attention-based hybrid network for structural nonlinear response prediction under long-period earthquake

To develop structures that can respond to severe seismic events, models and tools are essential for quickly and precisely assessing and controlling the structure's performance. Long-period ground motions may pose potentially significant hazards to the safety of high-rise buildings located in basins or alluvial plains. However, traditional regression-based methods and pure data-driven machine learning methods are insufficient to address this problem of response prediction, which is characterized by non-stationarity, nonlinearity, and scarcity of samples. To tackle this issue, we propose a novel semi-explicit physics-informed deep learning method. The method incorporates the physical information into the model, thereby achieving better prediction accuracy. Through numerical and experimental validations, including hysteresis experimental data, the actual seismic response record of a six-story hotel, as well as data from single-degree-of-freedom structures across various periods and multi-story buildings in Los Angeles, Seattle, and Boston, we verified the proposed method significantly outperforms traditional regression-based methods and data-driven machine learning methods in terms of accuracy, efficiency, and robustness.

A nonlinear structural pulse-like seismic response prediction method based on pulse-like identification and decomposition learning

Abstract Accurate prediction of structural responses under seismic action is important for the performance evaluation of structures. However, depending on the differences in the characteristics of ground motions, particularly whether they contain impulses, the seismic-response characteristics of structures may differ significantly. Hence, a new method, i.e., WD–AttDL, is proposed in this study to predict structural response under pulse-like ground motions. This method innovatively combines a wavelet decomposition-based velocity pulse-identification method with decomposition learning, where decomposed pulses and high-frequency features are used as inputs to the neural-network model, thus simplifying the identification of pulse features for the model. The decomposition learning module integrates different types of submodules, such as CNN feature-extraction, LSTM temporal-learning, and self-attention mechanism submodules. To reduce the nonlinear time-range analysis calculations required to generate training data, a screening method for impulsive ground motions based on time-series feature clustering is proposed. The accuracy and applicability of the proposed method are verified by numerically simulating three different cycles of reinforced-concrete frame structures and a three-dimensional masonry structure. Compared with existing structural seismic-response models, WD–AttDL synergistically integrates different modules and thus offers a higher prediction accuracy. In particular, it reduces the peak error of the predicted response, which is important for the evaluation of structural performance. Additionally, based on the response predicted by WD–AttDL, a vulnerability analysis of the structure under pulse-like seismic effects can be performed rapidly and accurately.

Doping engineering of NiO–Zn nanofilms for modulation of morphological structure and ultrafast nonlinear optical response at 515 nm

In this work, to investigate the metal doping on the third-order nonlinear optical properties of NiO thin films under femtosecond pulsed laser excitation, pure NiO and 2w,4w,6w,8w Zn doped-NiO nanofilms were prepared by DC-RF co-sputtering technique. Then, the nonlinear absorption properties and nonlinear refractive properties of the five samples were investigated using the femtosecond laser at a wavelength of 515 nm. The experimental results show that the nonlinear absorption and nonlinear refractive properties of NiO are enhanced by the doped metal as well as the effect of defects. In addition, by varying the pump light intensity, we observed the transition of nonlinear absorption from the coexistence of saturated absorption and reverse saturated absorption to reverse saturated absorption. We established a multi-energy level system to interpret the nonlinear absorption and nonlinear refractive results, which broadens the application of NiO thin films in the field of nonlinear optics.

Nonlinear Chiral Metasurfaces Based on Structured van der Waals Materials.

Nonlinear chiral photonics explores the nonlinear response of chiral structures, and it offers a pathway to novel optical functionalities not accessible through linear or achiral systems. Here we present the first application of nanostructured van der Waals materials to nonlinear chiral photonics. We demonstrate the 3 orders of magnitude enhancement of the third-harmonic generation from hBN metasurfaces driven by quasi-bound states in the continuum and accompanied by strong nonlinear circular dichroism at the resonances. This novel platform for chiral metaphotonics can be employed for achieving large circular dichroism combined with high-efficiency harmonic generation in a broad frequency range.

Full-field experiment-aided virtual modelling framework for inverse-based stochastic prediction of structures with elastoplasticity

Forecasting of stochastic ductile failures in fabrication and service stages are challenging tasks of advanced structures in practical engineering. Due to the prohibitive costs of repetitive experimental tests to quantify optimal failure-related parameters, numerous studies have turned to simulation-based uncertainty quantification. However, the credibility of these approaches is frequently doubted by the function-generated distribution of random data involved. Thus, an accurate assessment of the material parameters ascertains the appropriate estimation of uncertain parameters, which is essential for the risk/safety assessment of structures in different stages. In this paper, a full-field experiment-aided virtual modelling framework for inverse-based prediction of stochastic elastoplastic failure (EVMF-ISP) is proposed to deliver precise insights regarding the effective distribution range of mechanical parameters. To this end, all available experiment observations serve as the reference for assessing the prior and posterior probability density of the unknown parameters through the real-time inverse uncertainty quantification (UQ) module. The framework can be divided into three parts, where initially a pre-virtual model (PRVM) is formulated, and Bayesian inference is implemented to propagate the experiment observations backwards to ascertain the uncertain parameters. Then, an advanced multidimensional slice sampling method is developed to deal with the derived complex posterior probability density function (PDF) of mechanical parameters. In the end, a reliable stochastic elastoplastic analysis can be conducted with the revised uncertain samples and finalised with post-virtual models (POVMs) for the concerned structures. Such that, accurate and efficient determination of nonlinear response of structures can be directly predicted. The EVMF-ISP framework is logically presented and thoroughly illustrated with practical applications.

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

Time history seismic response prediction of multiple homogeneous building structures using only one deep learning‐based Structure Temporal Fusion Network

AbstractStructural response prediction under earthquakes is crucial for evaluating the structural performance and subsequent functional restoration. Deep learning provides the potential to rapidly obtain the responses by skipping the time‐consuming nonlinear finite element analysis. However, a single deep learning network may only predict the time history responses of one specific structure, resulting in redundancy and resource waste when building multiple networks for modeling different structures. Thus, this study proposes a Structure Temporal Fusion Network (STFN) that can predict responses of various homogeneous structures using a single network. The key concept is that the seismic waves and the structural characteristics, such as story numbers, are fused together to predict diverse time history responses. Two numeric experiments are conducted, including predicting responses of ideal single‐degree‐of‐freedom (SDOF) structures and regular multistory reinforced concrete frames. Furthermore, a series of ablation analyses are carried out to validate the network architecture. The results indicate that STFN can predict nonlinear time history responses of different structures with mean square errors in the magnitude of and for two experiments, respectively. The solutions also highlight the importance of fusing static characteristics for the modeling of various structures with only one network. The STFN presents a promising solution for time history response prediction across multiple structures in regions.

Nonlinear free vibration analysis of multi-directional functionally graded porous sandwich plates

Multi-directional functionally graded materials (MFGMs) have attracted significant research attention due to their advantages over one-directional FGMs. In MFGM structures, material properties can be tailored to grade in the required direction, overcoming practical problems like excessive temperature gradients or extreme deflections. This paper aims to investigate the nonlinear free vibration of MFG porous sandwich plates to improve their application in sandwich structures. The two outer layers of the plates are composed of three-directional functionally graded material (3D-FGM), with a bi-directional functionally graded material (2D-FGM) core layer. Additionally, the porosity distribution within the material matrix is assumed to be either even or uneven across the plate thickness. A higher-order finite element model based on Shi's plate theory and the von Kármán assumption is developed. The nonlinear free vibration frequencies are determined through the maximum vibrational amplitude using an iterative algorithm with a displacement control strategy. The accuracy and effectiveness of the proposed model are demonstrated through a comparison with published data. The results show that the vibration response is significantly influenced by various parameters. Specifically, increasing the material gradient indexes in the thickness direction enhances the frequency ratio, while increasing the gradient indexes in the length and width directions reduces it. Higher porosity coefficients in the core layer decrease the frequency ratio, whereas higher pore coefficients in the outer layers increase it. The additional knowledge gained from this study can help with future analysis and design procedures related to the nonlinear responses of these complex structures.

Multiscale modeling of friction hysteresis at bolted joint interfaces

Friction at connection interfaces plays an important role in understanding the nonlinear vibration response of jointed structures. A reliable friction contact model capable of reproducing nonlinear behaviors at the friction interface is critical in the design and optimization of jointed structures. In this paper, a multiscale friction model is proposed. This approach provides a novel perspective for improving prediction accuracy by combining the predictability offered by a physics-based model and the convenience of a phenomenological model. Specifically, this method considers the actual topography of joint interfaces by measuring the three-dimensional (3D) topography data with high-resolution instruments. The surface topography data is then processed to obtain the geometry data at different scales, and the finite element method is used to determine the physics-based multiscale contact pressure distribution of surfaces. The twofold Weibull mixture model is used to represent the contact pressure distribution and further determine the Iwan density function. The effectiveness of the proposed approach is validated by comparing the model predictions with the experiment results of a new as-built structure. Moreover, the effects of the surface roughness and waviness on the friction behavior are discussed.

Experimental nonlinear response of a new tensairity structure under cyclic loading

Pneumatic structures are recognized as promising thin-walled structures for their advantageous features such as lightness, portability, versatile design, and ease of installation. Although their bearing capacity under monotonic static loads can be formidable, their inherent dissipation capacity is low and thus entails significant limitations when counteracting dynamic loads. A novel tensairity structure is here proposed to overcome this drawback. The innovative design features a cylindrical inflatable element integrated with NiTiNOL cables wrapped around and affixed to a slender beam positioned along its generatrix. A laboratory-scale prototype is employed to assess how the structure behaves under cyclic loading in comparison to a standalone inflated beam and a conventional tensairity structure outfitted with steel cables. This experimental study delves into the influence of internal pressure and pretension levels of the metallic cables. Experimental results unfold a smooth softening-type hysteretic behavior under cyclic loading, which is accompanied by a slight stiffness degradation and a moderate pinching. The comparative analysis of the experimental results also demonstrates the substantially improved and consistent dissipation capacity of the presented novel concept of tensairity structure, which thus offers superior stability under cyclic loads. A parametric identification based on a modified Bouc–Wen model is finally performed to simulate the hysteretic response of the structure. A correlation is also established between the identified parameters of the phenomenological model and the internal pressure, type and cables pretension levels. The excellent agreement between numerical predictions and experimental force–displacement cycles other than those used for the parametric identification demonstrates the suitability of the adopted phenomenological modeling.

Deep neural network based time–frequency decomposition for structural seismic responses training with synthetic samples

AbstractTime–frequency decomposition is a powerful tool in assessing the dynamic behaviors of structures. Traditional time–frequency decomposition methods struggle with adaptability, and are limited in handling the structural responses with strong nonlinearity and closely spaced modes. In this study, a cutting‐edge approach based on deep neural network (DNN) is proposed to achieve a precise and adaptive time–frequency decomposition of nonlinear structural responses under seismic excitations. Remarkably, despite being trained on synthetic samples, the proposed method demonstrates outstanding performance in decomposing time–frequency components across various seismic response scenarios. Compared to variational mode decomposition (VMD) and synchroextracting transform (SET), the proposed method exhibited superior precision in time–frequency decomposition and excellent efficiency in parameter optimization. Moreover, the applicability of the proposed method to real‐world complex structures has been verified, which also shows promising generalization capabilities. Future research will aim to enhance the network performance by incorporating additional learning samples with diverse nonlinear characteristics.

A force-restricted inerter damper for enhancing the resilience of seismically isolated structures

An inerter is a mechanical device that generates a resisting force proportional to the relative acceleration between its two terminals. Several inerter-based dampers have been developed and studied to protect critical structures from the damaging effects of strong earthquake events. However, under high-frequency excitations, conventional inerter-based dampers may generate high resisting forces, which can result in excessive stresses in the supporting members and degrade the performance of the isolation systems. To overcome this issue, a novel force-restricted inerter damper (FRID) is proposed in this study for use in base-isolated structures. A simplified mechanical model of the proposed FRID was developed, which consists of a parallel layout of a viscous damping element and a nonlinear inerter element with a friction force restriction mechanism. The nonlinear hysteretic behavior of the FRID is discussed with an emphasis on the frequency dependence. Time- and frequency-domain methods were developed to evaluate the nonlinear dynamic response of the FRID-controlled structure. The performance of the FRID was investigated and compared with that of commonly used fluid viscous dampers (FVDs) and viscous mass dampers, when incorporated into base-isolated structures under short- and long-period ground motions. Parametric studies were conducted to investigate the influence of the FRID’s characteristic parameters on the seismic performance of controlled structures. The analysis demonstrated that the viscous mass damper and FRID provided superior control than the FVD on the displacement of a base-isolated structure, and the FRID is more effective than the viscous mass damper in reducing the control force and structural acceleration. This confirms that the proposed FRID is a promising, high-performance, and cost-effective device for enhancing the resilience of seismically isolated structures.

A computational study on the second-order nonlinear optical response of a new unsymmetrical oxovanadium complex

A new unsymmetrical N2O2 Schiff base oxovanadium (IV) complex, VOLPy, was synthesized with excellent yield and characterized using conventional methods. The crystal structure of the VOLPy complex was determined through X-ray diffraction, revealing a distorted square pyramidal coordination configuration around the central vanadium ion. The solid-state structure is stabilized by various non-covalent short contacts, generating complex 3D supramolecular network. The electrochemical properties of the VOLPy complex were investigated in different media, demonstrating diffusion-controlled reversible or quasi-reversible processes within the potential range of 200–1000 mV, involving a single electron VV/VIV reduction. The diffusion coefficients were calculated using Levich plots Ilim = f(ω1/2). Using quantum calculations at the CAM-B3LYP level with a 6-311G**/LanL2DZ basis set, we systematically assessed various structural parameters, electronic properties, linear and nonlinear optical responses at static and dynamic regimes for oxovanadium complexes, V(V)OL and V(IV)OL, in both gaseous and solvent environments. The results reveal a robust alignment between quantum calculations and experimental data, with only minor deviations. This study anticipates that these specifically designated complexes hold substantial potential as excellent candidates for second-order nonlinear optical (NLO) materials.

A new metamodel for predicting the nonlinear time-domain response of offshore structures subjected to stochastic wave current and wind loads

Offshore structures are subjected to stochastic loads from wave, current, and wind. A long-term response analysis is important for evaluating the structural safety; however, it is computationally demanding to perform the large number of nonlinear time-domain simulations. Metamodeling is an attractive prospect, but there are two existing obstacles to overcome. First, existing metamodels are mostly confined to a single sea state and are unable to predict the response for different wave directions. Second, for floating systems, the inputs are usually vessel loads/motions, which are a priori unknown. This paper develops a new metamodel framework for accurately predicting the time series response under short-term uncertainties from the stochastic process, and seven long-term variables, namely the significant wave height, spectral period, wave direction, and speeds and directions of current and wind. The exogenous input is based only on the environmental variables, which can be predefined. The proposed metamodel is implemented on a floating system and used to predict the time series of riser stress, the extreme stress response and fatigue damage. Four cases with increasing number of long-term variables are tested. Excellent agreement is found between the metamodel prediction and numerical simulation even for the most critical case with all variables included.

Next-generation non-linear and collapse prediction models for short- to long-period systems via machine learning methods

Since the 1960 s, a cornerstone of earthquake engineering has been estimating the non-linear response of structures based just on lateral strength, modal properties, and the anticipated seismic demand. Over the years, several studies have quantified this empirical relationship and integrated it within seismic design and assessment methodologies. These have been widely accepted for practical application and adopted in building codes worldwide. While these models work reasonably well, there are still areas in which improvements can be made, especially concerning their robust quantification of uncertainty. This is mainly due to the amount of data used to quantify these empirical relationships, the choice of functional forms during the fitting, the model fitting and testing process, and how the ground motion shaking intensity is characterised. This study tackles these issues via the non-linear analysis of single-degree-of-freedom oscillators to train several machine learning (ML) models. This was to examine the accuracy and applicability of such models within a seismic engineering context and explore potential gains in quantifying the non-linear response of structures via next-generation intensity measures, namely average spectral acceleration, Saavg. The results show that the Decision Tree and XGBoost models worked well across a broad range of periods, accurately predicting collapse and non-collapse responses. Appraising these with existing models showed a notable improvement all around. It indicates that the models based on data-driven ML approaches represent a positive step and can be seamlessly integrated with seismic analysis methodologies utilised worldwide. Subsequently, a Python-based library of these XGBoost ML models was developed and made available online to foster practical application.

A Ball-Contacting Dynamic Vibration Absorber with Adjustable Stiffness and Nonlinear Characteristics

Structural vibration has always been a major concern in the engineering field. A dynamic vibration absorber in the form of contacts with adjustable stiffness (CDVA) offers effective vibration suppression and can improve conventional dynamic vibration absorbers with high sensitivity to frequency deviation and difficulty in adjusting the frequency. In this research, first, based on the theoretical model of the contact between a rubber ball and an inner cone, the feasibility of changing the axial contact state to change the structure’s natural frequency was verified using an ANSYS simulation. A theoretical model of the static contact stiffness between the ball and the inner cone was constructed using Hertzian contact theory and Hooke’s law, and a theoretical model of the cubic nonlinear elastic restoring force was used to characterize the stiffness properties of the rubber ball during compressive rebound. The steady-state frequency response equations of the main vibration structure were derived using the averaging method in conjunction with the two-degree-of-freedom dynamics model, and the stability of the solutions to the frequency response equations was obtained in conjunction with the stability determination criterion. Then, the impact of the CDVA’s design parameters on the nonlinear dynamic response of the primary vibration structure was simulated and analyzed. The resulting findings can serve as guidance for designing dynamic vibration absorber parameters. Based on the principles of ball-inner cone contact, a dynamic vibration absorber structure was proposed. A design test was conducted to verify the correctness of the contact stiffness model, and an experimental study was carried out to investigate the law of change in the dynamic stiffness and damping of the principle structure of CDVA under dynamic excitation conditions. Finally, the vibration test platform of the solidly supported beam structure was constructed, and vibration suppression tests of the CDVA in different compression states were conducted to investigate the tunability and feasibility of CDVA vibration suppression. The results showed that the dynamic vibration absorber had good vibration absorption characteristics and could be used for single-mode vibration suppression of multimodal main structures.